Railway rail



De- 4, 1951 G. R. BURKHARDT RAILWAY RAIL Original Filed April 9, 1942 WIDTH 0F ANGE C RATIO WIDTH oF WEB. u

INVENTOR GEO. BURKHARDT Patented Dec. 4, 17951 RAILWAY RAIL George-R. Burkhardt', chicago, nl.

Application December 15, 1944, Serial No. 568,309

claim. (o1. zas- 125) This case is a continuation in part of Vmy pending application, Serial No. 438,311, now abandoned, filed April 9, 1942, and relates to railway rails of the Vignoles type, i. e., rails which are of substantially T-shapein cross section, and has particular reference to an improvedV distribution of metal in such rails, for the purpose of reducing stress concentrations therein, particularly in and about the head-web and base-web fillets thereof where, according to prior rail designs, undesirable high and dangerous Vstress concentrations have occurred.

Stress concentration in and about the headweb and the base-web llets of T-rails causes fatigue of metal in these locations and are conducive to split heads, cracked webs, and other types of rail failures. In this connection, the A. R.. E. A. formulae for stresses'in railway rails (page 886, A. R. E. A., volume 19)' are based on the assumption that the stress is distributed according to the law that it increases directly as the distance from the neutral axis. However, the abrupt changes occurringA in T-rail sections results in discontinuity in the distribution of stress. Accordingly, the said A.- RLE. A. formulae for calculating stress in rails is, in many cases, not even a rough approximation of the maximum stress concentrated in the head-web and the base-web fillets of a Adynamically loaded rail. In other words, rail design practices heretofore in vogue do not take into consideration all of the factors essential for reduction in stress concentration in and about the head-web and the base-Web fillets of T-rail in that they do not suiciently consider the relationship of thedistribution of metal in the web at its junction with the head and the base of the rail as well as the relation of the Width and depth of the head to the width'of the web. These facts teach the necessity of a more fundamental study Aof the stress conditions in the junctures ofA head and studies have been made which would establish the effect of proportions of the head, web and fillets of the rail section on the resulting stress concentrations. The study of the effect of these proportions was made from the measurements of strains in the rail as shown by two dimensional photoelasticand strain gage tests on rails and from membrane analogy. Tests were. made on models with vertical loads applied accentrically to the head. The baseof ther rail was uniformly supported in some cases and in other kcases the base was supported only ati the edges to simulate the conditionslresulting from the. .usual concave 2 tie plate. Investigation was made of the stress in models in which the ratio depth of ange to width of webA was kept constant and the ratios of width of head to width of web, and ratio of radius of iillet to width of web varied. Investigation was also made of the effect of deep flanges. Therefore, the primary object of the present invention is to provide a T-rail having an economical and eiiicient metal distribution involving anovel ratio of width-of-web at the junction of the head-web and the base-web fillets therewith to the radii of said head-web and base-web fillets, combined with a width and depth of the head, such that high and dangerous stress concentrations in and about the head-web and the baseweb fillets and throughout the rail are avoided. That is to say, while the stress concentration factor is the ratio between the stress in the fillet and the stress in the web, this factor in a shape such as a rail, where the change in shape fromV web to head and web to base is rapid, is a simultaneous functionof the ratio width and depth of head to width of web combined with a novel radius of fillet to width of web ratio, and these ratiosl are critical in mutually producing a safe and efcient rail..

According to the present invention, the yradii of the head-web iillets are substantially equal to the width of the web at the juncture of the head and the web. In other words, the head-web fillets of a rail produced in accordance with the present invention have considerably longer radii than the head-web iillets of rails produced in accordance with prior practice. As a consequence, wide bearing areas .are aiforded to be engagedv by the heads of splice bars of the Headfree type and these v wide bearing areas are conducive to longer life tribution and proportion of parts hereinafterl o more fully described, illustrated in the accompanying drawings, and defined in the appended claims. Y

In the accompanying drawings: Figure 1 is an end elevation of a rail, in full Y Vlines, having its metal distributed in accordance with the present. invention while the broken lines show the distortion resulting from loading the rail in the manner described.

Figure 2 is a chart showing a series of graphs indicating the results of studies of diierent rail sections, and teaches the ideal ratios between radius of fillets and the width of web and ratios of width of head to Width of web at the juncture with the fillets.

Referring to the drawings in detail, it will be observed from Figure 1 that the present rail is of the Vignoles or T-type and comprises, as usual, a head I, web 2, base 3 and head-web and baseweb fillets 4 and 5, respectively, at the junctures of the head and the base with the web. Also, dimension lines with reference letters are shown to describe the ideal proportion of the metal distribution of the present invention.

Generally the letter C has been used to designate the width of anges, treating the head I as Well as the base 3 as such, and likewise R and U are used in the equations to designate the radii of the fillets and Width of web at the juncture of the fillets therewith respectively, so that the graphs of Fig. 2 will apply equally to the head or the base and M generally designates the depth of the anges. However, as will be seen from the drawing, an appropriate subscript is used in each case to designate the specific ange, radius or web thickness. For example, CH designates the width of the head and CB designates the width of the base, while the radii of the head fillets 4 and base fillets 5 are respectively designated as RH and RB, and the Width of the web 2 at the junction of said fillets with the web is also respectively designated as UH and UB. The depth of the head I is indicated as MH and the depth of the base is shown by the reference MB. Also the width of the head along the top line of the fishing is designated as CF.

The outer sides of the web 2 are each of a substantially flat concave curvature as conventional in rails of the Vignoles type and the point of minimum thickness of the web is between the head fillets and base llets along a horizontal line passing through the center of curvature i the arcs of greatest radii of the web on opposite sides of the vertical center line of the cross section of the rail. For example, in Fig. 1, the dimension T represents the minimum width of the web, and the dimensions UH and UB represent the maximum width of the web. The ratio of T to overall rail heights is empirically determined.

As previously indicated, the present invention relates to a new distribution of metal in the web, head and base of the rail where the factors to be considered are the relationship of the width and depth of the head to the width of the web and the radii of the fillets to width of web. The graphs show that these ratios simultaneously affect the stress concentration factor.

Referring first to the feature of the radii of the fillets 4 and 5 joining the web 2 to the head I and the web 2 to the base 3 of the rail and assuming, for example, that RH and RB are the radii of the fillets, and UH and UB are respectively the thickness of the web at the junction with the head and base fillets, it has been found that stress concentration in said fillets inGreaSeS with-decrease of the ratio H H o, m UH UB below one or unity and also increases again with increase of said ratio above one or unity. In other words, it has been found that stress concentration in said fillets decreases rapidly to a minimum when l (z]=011e and remains substantially a minimum within a range of said ratio of not less than .8 nor more than 1.6.

Accordingly, the ratio of the radius RH to the width UH in the present rail is substantially unity or within the range stated, and likewise, the ratio of the radius RB to the width UB of the web is substantially equal to unity or within the range stated. The graphs show that the stress concentration factor is lowest when R -LO and that R Q -O and U-LG are the desirable limits to be placed on this ratio. The ratio of is made because the stress concentration factor is lowest at this point. The graphs show a substantial equality in the stress concentration fac tor between the ratio R R R It is to be noted that there is a sharp increase in the stress concentration factor for the ratio In other words, 0.8 is just below the knee of the curve which is substantially horizontal between 0.8 and 1.6. At the point where thel ratio of the curves again turn upward at an increased rate.

Referring now to the Width CH of the head I and the Width of the base CB in relation to the width UH or UB of the web and the radii RB and RB of the fillets, my studies of rail stress by membrane analogy show that stress concentration increases rapidly when the ratio of width of head C to widthV U of web exceeds four, and likewise stress concentration increases again when the width C of the head is less than two and one-half times the Width U of the web 2. As shown in Figure 1, the overall height of the rail is designated as A which is not more than 11A; times and not less than the width CB of the base to provide against overturning by the resultant of vertical and lateral loads and being greater than the width CB of the base section which is not less than twice the width CH of the head section I.

contains points obtained by investigating the;

i old type rails, for example, the A, R. E. A. 112 1b.

wlmi

sections and modicatins thereof such as ref cucine the width of the head. The dotted line, marked M... fj- 2,4 and and and

-was drawn through points obtained from meas urements of rails strained as shown in Fig. 1. The line marked TV-,v2.4 and Utah() .Shows that lowest stress concentration factor results `from equality between-the thickness cf the web and radius of fillet.

The line marked %f.-4.O and 1.1.0 substantially horizontal because the bending ef the danses is negligible when My analysis of stress in railway rail with l.curved webs shows that the shearing stress inthe web increases inversely as the radius of the curves. also, when a llet radius is .employed equal to the width of web at the point of compounding, stress concentration is a minimum. Furthermore; my analysis demonstrates that the transition .of the stress from web to head is less critical when the radius 0f the iillet equals the Width of the Web.

My experience with failed rails, particularly failure in the base, shows that concave tie plates and convex rail bases cause the typeof bending in the base shown in Figure 1. Accordingly, it is important that the radius of the fillet Rn is not less than 0.8 times the depth of the base at the juncture or point of tangency with the llet. Also the radius of nllet should not be more than 1.6 times the depth of base. The ideal ratio is of course 1.0 so that at the'point of tangency With fillet the width `of web `should equal the depth'of base.

Thus, the graphs of Figure 2 teach the ideal ratios between radius of fillets and the Width of web and ratio of Width of head to width of web of the juncture with the llet. lThe sever-ai illustrations given denitely show that these ratios simultaneously affect the stress concentration factor. The maximum stress, a max, occurring in the iillet joining head and web and web and base can be expressed as a multiple of the nominal stress, fr nom, in the web. Thus a maxEk cr nom where lc is the stress concentration factor. V

The studies undertaken showed that the following factors contribute to an increase-in the max stress, amax.

With respect to the relation of the point of load te fillets, i. e., the ratio of width of flange te width et web as shown in the graphs, the sin sbt edge vai the eress .section eppesite the fillet in a slight increase in' the stress concentration factor, when is less than `3 and a substantial :increase when is greater than 4.0. Tests by membrane analogy show that the maximum shearing stress occurs about at the center of the llet and that there is a notable increase in stress from the point where the llet is tangent to the flange to a point in the center of the fillet.

,As tothe ratio of the depth .of flange M to width of web U, the graphs show that the lstress concentration becomes smaller with an increase in the ratio A/: yU

The ratio lf U is :the ratio 1between maximum :depth of head and minimumwidth ofweb. When er less then bending of flanges Ais .a factor in the strain. The minimum lower limit lef is 2.0 to prevent the stress resulting from bending of the flanges of the head from exceeding the endurance of rail steel. In Figure 1 the depth of head Mn is shown as twice `the thickness of `the web at the iuneture of the head-web fillets therewith as must-rated by .UH- Thus, according to the drawing, the lowest limit of the ratio When this bending can be disregarded. The stress concentration, then, increases as the ratio 7 Tests have been shown that the shapes of the curves or graphs are similar when the stress concentration factor is platted as a function of the ratios UU U In a rail this factor is a simultaneous function of all of these ratios both in the head and base. The most important ratios in a rail are E U coupled with gli. and .Q -B.. UH UB The most economical and satisfactory metal disL tribution results from making not less than 0.8 nor more than 1.6 and at the same time making dus the juncture with the head-web fillets. If R=U then the width CF of the head along the top line of the fishing equals CF=3U-g=%-=2%U approx.

As shown in Fig. l, the improved metal distribution described provides for an increased bearing for the head of the joint bars, and also maintains in the improved Headfree type rail, the desirable functional phase of the standard comparable Headfree rail.

I claim:

1. A Vignoles type rail having a head section, a base section, a web section, head-web llets and base-web fillets, the sides of said web section being of a substantially flat concave curvature, the point of minimum width of said web lying between the point of tangency of the headweb and base-web llets with the web and being along a horizontal line passing through the center of curvature of the arcs of greatest radii of the web on opposite sides of the vertical center line of the cross section of the rail, the width of the web at the juncture with the head-Web and base-web llets being not .less than said minimum width, the radius of each of said fillets being not more than 1.6 and not less than 0.8 times the width of the web at its juncture with the llets, said head section at its thickest point having a depth of not more than 4 and not less than 2.4 times the width of the web at the juncture of web and head-web iillets, the maximum width of said head being not more than 4 times and not less than 2.5 times the width of the web at the juncture of the web and head-web llets, the overall height of the rail being not more than 13 times the minimum width of web, not

8 more than 1% times and not less than the width of the base to provide against overturning by the resultant of vertical and lateral loads and being greater than the width of the base section which is not less than twice the width of the head section.

2. A Vignoles type rail according to claim 1 wherein the radii ofthe iillets are equal to the width of the web at the point of tangency of said fillets with said web.

3. A Vignoles type rail construction according to claim 1 wherein the depth of the base section at the point of tangency of the base-web fillets therewith is not less than 0.8 or more than 1.6 times the radius of the base-web llets.

4. A Vignoles type rail construction according to claim 1 wherein the depth of the base at the point of tangency of the base-web llets therewith is equal to the radius of the base-web llets.

5. A Vignoles type rail having a head section, a base section, a web section, head-Web llets and base-web iillets, the sides of said web section being of a substantially flat concave curvature, the point of minimum width of said web lying between the point of tangency of the lhead-web and base-web fillets with the web and being along a horizontal line passing through the center of curvature of the arcs of greatest radii of the web on opposite sides of the vertical center line of the cross section of the rail, the width of the web at the juncture with the head-,web and base-web fillets being not less than said minimum width, the radius of each of said fillets being not more than 1.6 and not less than 0.8 times the width of the web at its juncture with the fillets, said head section at its thickest point having a depth of not more than 4 and not less than 2.0 times the width of the web at the juncture of web and head-web llets, the maximum width of said head being not more than 4 times and not less than 2.5 times the width of the web at the juncture of the web and head-web llets.

GEORGE R. BURKHARDT.

REFERENCES CITED lThe following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date 2,260,211 Burkhardt Oct. 21, 1941 FOREIGN PATENTS Number Country Date 1,856 Great Britain May 20, 1875 OTHER REFERENCES Stress VConcentration Produced by Holes and Fillets, by S. Timoshenko and W. Dietz, American Society Mechanical Engineers, Transactions 1925, page 212, section 35 et seq.

Torsion in Structural Beams, by F. L. Ehasz, Lawrence Calvin Brink, Research Fellow in Civil Engineering, Lehigh University.

Railway age, December 12, 1942, pages 963-967, Vol. 113, No. 24.

Steel Rails, by William Sellew. Plate No. XVII, deposited in the U. S. Patent Ofce Library June 26, 1941, printed in 1913 by Van Nostrand Co. of N. Y. 

